In many defense and other applications, a first detector system observes movement of an object and, based upon this movement, provides information to a second system that has defensive capabilities or which can otherwise engage the object. The first detector system may be a radar or other active range determination system and may be a central detector system or other remote sensor that observes the movement of the object and provides information to the second system. It is of paramount importance for the first system to identify a sector within which the second system should search for the object because it is critical for the second system to locate the object as quickly as possible, especially in the military arena when defensive tactics may be exigently required. This is true for various applications regardless of the action desired to be taken by the second system with defensive or active engagement capabilities and also applies to any of various first detector systems that track positions of objects in space, estimate the positions of the object and assign a degree of uncertainty to the position estimates.
The second system with defensive or active engagement capabilities that uses the information provided by the first system to determine where to search for the object, typically includes an active range determination system itself such as a radar, but requires location information from the first system in order to know where to search for the moving object, especially in exigent circumstances, so that it may respond efficiently and quickly. It would therefore be desirable for the first system to accurately identify a limited space sector within which the second system should search for the object.
The tracking and monitoring of such moving objects is advantageously and conventionally done using the azimuthal angle of the object's overhead position detected or estimated by the first system with respect to an origin O, with the azimuth being the angle between a reference radius N and a vector representing the perpendicular projection of the object's position on the horizon. It is desirable for the first central tracking system or remote sensor to provide information to the second system that identifies which space sector to search, the space sector advantageously identified as an arc of a circle centered on origin O, according to common convention.
Conventional methods consider only the progression of estimates or measurements and assume that any intermediate measurement must lie between the extrema. Consequently, when evaluating whether an angular interval, i.e., an arc of a circle centered at origin O, contains a reference angle, the occurrence of an intermediate measurement indicating the incorrect arc will result in an incorrect conclusion.
One conventional method for estimating the current position of a moving object with respect to a central origin, is a method that relies on progression of measured or estimated locations to predict the current position. This method utilizes average values in sequential measurements but includes limitations, however. For example, the “average” values in sequential measurements of a progressive function (f(t) monotonic) with superimposed random noise, where average values lie between extrema defining an arc of a circle, may occur out of sequence due to uncertainties. Measurements of angular displacement of a trajectory of a moving object over a time interval result in a series of sequential position estimates between extrema, e.g. the angles corresponding to the position estimates at the earliest and latest observation times, which define the end points of an arc enclosing intermediate angle measurements. When these estimates contain noise, such measurements may produce an incorrect sequence of angles of measurement. Particularly for noisy radial estimates, intermediate angles of measurement may appear outside the extrema. Logically, limits that define an arc of a circle divide space into two regions: a clockwise arc between the extrema and a counterclockwise arc between the extrema. Due to the limitations in relying solely on the progression of the “average” values, an error may result in the determination of which of the two possible arcs defined by the extrema, contain intermediate unmeasured values of the function, and possibly the moving object.
When moving objects are tracked by a central observer, it is also desirable to determine if a reference angle, i.e., an azimuth or elevation such as due North, has been crossed or whether a radial vector is included by a range of solid angle measurements, i.e. whether the bounds of the identified search sectors contain North or another radial vector.
The present disclosure addresses the above-identified shortcomings and needs.